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Charge2

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## Homework Statement

This is a interesting (morbid) problem from Simmons- Calculus with Analytic Geometry.

In a certain barbourous land, two neighbouring tribes have hated one another from time immemorial. Being barbourous peoples, their powers of belief are strong, and a solemn curse pronounced by the medicine man of the first tribe deranges and drives them to murder and suicide. If the rate of change of the population P of the second tribe is ##-\sqrt{P}## per week, and if the population is 676 when the curse is uttered, when will they all be dead?

Intial Conditions

##P(0) = 676##

## Homework Equations

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None

## The Attempt at a Solution

*##\frac{dP}{dt} = -\sqrt{t} = -t^{1/2} ##.*

Separating the differential equation,

##dP = -t^{1/2}dt ##,

Then, by intergrating,

##\int dP = - \int t^{1/2}dt ##

##P = -\frac{2}{3} t^{3/2}+ C ##...(1)

Solving for C at t= (0) or P(0) weeks, when the medicine man uttered his curse,

##676 = -\frac{2}{3} (0)^{3/2} + C ##,

##C = 676##.

Subbing this in (1)

##P = -\frac{2}{3} t^{3/2}+ 676 ## ...(2)

Rearanging (2) for t, when P = 0 because the second tribe are all dead,

##0 = -\frac{2}{3} t^{3/2}+ 676##,

##-676 = -\frac{2}{3} t^{3/2}##,

##t = (\frac{2028}{2})^{2/3}= 100.93 = 101## weeks .

Is this correct. Or have I made a massive error? Seems like they need a more powerful medicine man...

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